Popular Website Logic Puzzle

The first clue tells us that the first three sites visited are Amazon, eBay, and Taobao, in that order.

We can’t do much with the eBay or Taobao clues yet, but the Amazon clue tells us that Sina has to be #4, since it was visited consecutively with Taobao and we know Taobao is #3.

The Sina clue tells us YouTube is #5 (2+3). BBC Online could technically be 23 or 32, but since there are only 25 answers, we know it must be 23.

Let’s take the BBC clue first. We immediately rule out Column 1 and 3 because their sites aren’t in order top to bottom. Column 2 is also out because 2, 4, and 5 are already taken. That leaves us with columns 4 and 5 as possibilities. Time to look at an earlier clue, namely the eBay clue. We know the search engines were all visited in one chunk of browsing, but no two of the Google sites can be visited together. There are 7 search sites, 4 Google and 3 non-Google, which means the order must go Google-notGoogle-Google-notGoogle-Google-notGoogle-Google. And we know the main Google site was visited at #13. Therefore all the Google sites have to be odd numbers, and the non-Google search sites even numbers…but Bing and Google Germany are two squares apart in column 4. It can’t be the column that’s in order, so we’re left with Column 5 being 21-25 top to bottom.

And a quick easy one: the YouTube clue tells us Sporcle ends in a 5 and Wikipedia ends in a 1. We’ve already got sites 1 and 21, so Wikipedia must be 11.

IMDb tells us that every number in column 2 is less than 10. We already have 1, 2, 3, 4 and 5, so that means the last three squares in column 2 must be three of the four numbers 6, 7, 8, and 9. But Taobao tells us that the squares in rows 2 and 4 must be even numbers (since row 3 is the one that has both even and odd numbers), so we know 6 and 8 are in the squares Twitter and Blogspot in some order. But which order? That requires the Flickr square. It says one row has two pairs of adjoining squares where the left-hand square is half the right-hand square. That already limits us to the even rows, 2 and 4, since an odd number can’t be twice another integer number and the mixed even-odd row doesn’t have any such pairs now and nothing we put in Bing would make it work. It also can’t be row 2–the Wordpress square can’t be 11 (Wikipedia) or 8 (must be in column 2), so the two pairs of squares would have to be Facebook&Twitter and Twitter&Sina–but that would mean they’re 1, 2, and 4, and we know they can’t be. So the row with the two pairs is row 4.
We can also work out that the number in row 4 can’t be 6. If it was, our choices for pairs would be: Yahoo! 3 and Blogspot 6 (disallowed by Taobao’s clue & eBay’s number); Blogspot 6 and Yandex 12 (possibly okay)…but then what’s in the tumblr square to make a second pair? It would have to be double the number in Yandex–12–so it would be 24, but that’s taken; or it could be half the number in Flickr–24–but that’s 12 and we just said that had to be in Yandex! So Yandex can’t be twelve. That means, if Blogspot is 6, the two pairs would have to be Yandex&tumblr and tumblr&flickr, but then that would be Yandex 6, tumblr 12, Flickr 24 and we started with the assumption that Blogspot was 6. No combination of two pairs is possible then, so by elimination Twitter is 6 and Blogspot is 8.

Let’s finish off Flickr’s clue. We know that Yahoo! and Blogspot can’t be a pair–we already have a number 4. We also know that Yandex&tumblr and tumblr&Flickr as the two pairs don’t work, because that means Yandex is 6 and we know it isn’t. The two pairs are therefore Blogspot&Yandex and tumblr&Flickr, so Yandex is 16 and tumblr is 12.

The Sporcle clue tells us the sums of the five columns. Column 2’s numbers currently add up to 18; if the sum were 54, LinkedIn would have to be 36, but the max number is 25 and the max for column 2 is LinkedIn (IMDb’s clue). The problem just gets worse for the larger sums. The sum for column 2 is therefore 25 and LinkedIn is 7.

Now, we can apply Sporcle’s clue to column 1. The current sum is 29. We know that Yahoo! and Facebook have to be even numbers (Taobao’s clue), so the overall sum will be odd, but the column that sums to 25 is column 2 and the column that sums to 115 is column 5–the only even sum left is 63. Facebook’s number plus Yahoo’s number must be 34, but we know that all the even numbers less than 10 and greater than 21 are taken–our only choices are 16 and 18 or 14 and 20.
eBay’s clue comes back in here. We know that the search engines have to be 7 consecutive numbers, and they have to start and end with Google sites and therefore start and end with odd numbers (as discussed a few steps back). We know Google is 13, and we know Wikipedia (not a search engine) is 11–so the search engines start at #13 and run to #19. Facebook is not a search site so it can’t be 14, 16, or 18, and we said the only possibilities were 14, 16, 18, or 20. Facebook is 20, so Yahoo! is 14.

We only have two non-search engine sites left: Wordpress and pinterest. The numbers we have yet to assign are 9, 10, 13, 15, 16, 17, and 19. 13-19 are search engines per eBay’s clue, as discussed in the previous step, so Wordpress and pinterest must be 9 and 10, and Taobao’s clue tells us pinterest is odd and Wordpress even, so pinterest is 9 and Wordpress is 10.
We can also quickly take care of Bing–it’s the only non-Google search engine left, so it must be 18.

Sporcle’s clue plus the columns we’ve already filled in tell us that column 4’s numbers must sum to either 54 or 68. The numbers we have already sum to 59, so since 5 is already taken, Google Germany is #19.
Wordpress’s clue says that Google India came before Google Japan, so Google India is 15 and Google Germany is 17, the only two numbers we haven’t assigned yet.